Questions tagged [beam]
Questions about the theory and applications of structural elements designed to resist bending.
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Justification for choice of beam stiffness at pinned far-end member
I’m reading off an example provided by the ICE structural analysis book, specifically example 4.7 (moment distribution method) I dont seem to understand why the stiffness from member D-C is 4EI/L ...
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Beam deflection for FEA model validation
I'm trying to validate an FE model that I'm using by comparing to a simplified analytical solution to the problem.
The part I'm analyzing is a lug that is constrained on one end and has a point load ...
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Mechanics of Materials Method for Curved Beam with Different Centers
The common curved beam theory covered is the Winkler method (e.g. in Johnston and Beer, or Boresi and Schmidt). As can be seen by reading any derivation, this method applies to beams with a common ...
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Rigid frame deflection and material selection
I'm building a frame that will receive a point load mid span (likely it won't be but want to design for worse case).
The frame is 1.5 x 0.095 square tubing, and it will be skinned with 14ga on one ...
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The Effect of Accelerometer Position on Modal Analysis of a Cantilever
We have obtained the first two vibration modal frequencies of a composite cantilever (33 gm). We placed the accelerometer (3.4 gm) near the fixed end and the two frequencies were F1=30 Hz and F2 = 256 ...
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Ratio of length to baseplate bolt pattern to assume that a joint is pinned
I have a truss tower that is attached to a hoist arm by a baseplate. The truss tower is 80ft long and the bolt pattern of the baseplate is a 1ftx1ft square. Is it valid to assume that the joint ...
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Which formula to use to calculate the main vibratory frequencies of a wooden joist floor? (8 Hz?)
When a wooden floor joist is a little undersized, there is a vibration phenomenon when walking on the floor.
In some forums, I've often seen a frequency of 8 Hz mentioned when walking on the floor, ...
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Extension of a cantilever beam composed of unbonded layers
The question of the magnitude of the vertical deflection of a cantilever beam composed of unbonded layers has been posted here, but I was wondering if there is an analytical way to solve for the end ...
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Shearing Stress in a Beam with Torsion
In "Theory of Elastic Stability" by Timoshenko and Gere, the authors say for a beam in pure torsion,
For a beam of thin-walled open section it can be assumed with
reasonable accuracy that ...
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Benchmarking Geometrically Exact Beams: Clarification Needed on Material Density?
In an early paper on Simo, I came across an example titled "Cantilever 45-degree bend subject to fixed and follower end load". A force of $600N$ and $300N$ was applied at the end, resulting ...
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Warping deformation for arbitrary cross-section under torsion
Title says it. I wish to learn the approach for programming (with FE, or with alternative discretized models) the warping deformation for each point in an arbitrary cross-section, knowing the contour ...
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Calculating Admissible Shear stress with a uniformly distributed load and a point load
I have the following equation for calculating the Admissible shear stress for a uniformly distributed load.
$$\tau_{adm} = \frac{3}{2}\cdot \frac{F\cdot L}{2b\cdot h}$$
where
$F$ = kN/m
$L$ = ...
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Load distribution for a load centered over the length of the middle joist in a 3-joist system
I'm not an engineer, but I'm trying to understand the correct analysis for what seems like a pretty simple case.
I'd like to know what the effective load on the middle joist is.
...
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Determine the temperature required for expanding or bending?
Is there any possible way to calculate the temperature required for a metal to expand or bend with dimensions?
For example, take Mild steel with a length of 100mm, width of 150mm, and thickness of 2....
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How can I calculate the maximum center load on a horizontal cellular glass tile; supported along its edges, before it breaks?
Insulating cellular glass boards or tiles are designed to sit on a flat load-bearing surface. I want to consider the situation where the base is concave so the tile is only supported on its edges. I ...
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Determining the critical load of a fixed beam with non-uniform cross-section?
I am a computer scientist, not a mechanical engineer, so it is absolutely possible that I am missing some basic understanding here.
I have a beam that is fixed in both ends and my goal is to ...
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Theory of large deflection of (cantilever) beams
As the simplified theory of beam deflection, taught in typical mechanical engineering courses (in Germany its called first order theory), is limited to small deflections, I want to look into the ...
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Optimal shape for cantilever beam subject to body weight only
How can I find the optimal shape of a cantilever beam subject only to its own weight, and having the following restrictions?
The cross section is a rectangle
Only the height of the rectangle can vary ...
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Spring constant of angled beam
I'm trying to solve for the dynamics of three blocks, shown below. Two blocks are pushed into a central shuttle, and their force is transmitted through a thin angled beam/pawl. The pawl bends when ...
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Searching for geometric modeller to investigate behaviour of beam when deflected
I have the scenario where I wish to model the movement of a simply supported beam under a central point load. I've done some stuff in R Studio to come up with deflection plots and that's fine. In ...
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How to compute the resistance of this metallic part (steel angle iron), for a joist fitted in an I-profile beam?
Let's say we have an oak joist (15 cm x 15 cm x 370 cm), which is "fitted" in the profile of an I-profile beam (height 140 mm, width 66 mm), and the surface where the joist is laid is too ...
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Moment of a unimorph cantilever
I know as a general rule that the moment is the integral of stress multiplied by cross-sectional area (gives force) with the perpendicular distance from force, as mentioned in the lecture notes :
Now,...
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How to relate stiffness, weight, moment of inertia to obtain a stiffer system?
The technical field of the question is gantries in CoreXY 3D printers, where a gantry moves in Y direction and it holds a carriage sliding in X direction. In the following image, X is horizontal and Y ...
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Is a vibrating Euler beam supposed to behave in this way?
I am a student of mathematics and for my modelling seminar, I need to dip a little bit into engineering in order to model the movements of a suspension bridge under influence of wind. This will be ...
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Traction boundary condition : Cantilever beam
Since I don't have that much experience with solid mechanics and stress theory, I am a little confused about my understanding.
My problem is a basic solid mechanics problem of cantilever beam bending.
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Thermal Expansion and Stress in a Heated Beam
Consider the case of a beam that is supported in such a way that expansion can occur freely. Suppose that the beam is heated in such a way that the temperature varies with the depth of the beam. Let $...
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Correct beam theory for calculating radial force in bearing due to a bending moment in beam?
I am designing a cylindrical shaft that has a round disc at its top. I am hoping to seat this shaft in 2 radial bearings and couple to a motor. The image below gives an overview of the loading diagram....
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Predicting breaking force of beam per length based on one testing
I've made a plywood carbon sheet and tested its breaking force, for a 200mm long, 50mm wide, 16mm thick it was 100kg +-
I was wondering if it's enough to help me predict what will be the breaking ...
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Truss beam like structure strength per height
The second beam is 2x the height of the first one.
Is 1 stronger then 2 to bending force (arrow shows direction, supported on the sides)?
If it does, I'm trying to figure out why, because they both ...
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In the context of Beam Deflections If the moment curve has a discontinuity, how do we account for it in the slope and deflection curve?
In reality if we load a beam within the elastic range of the material, it forms a curve that can be represented by a mathematical equation. But if the moment curve has a discontinuity it must mean ...
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Calculating deflections on an inclined beam
I'm applying a force to a stepped inclined beam (that's what I'm calling it; don't know what the correct technical term would be) in which it's essentially a cantilever with the first section angled ...
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What is the equivalent rotational/angular stiffness of a beam
I'm trying to model a larger system and working through a conceptual issue. I'm familiar with the concept of expressing the stiffness of a beam as an equivalent spring stiffness like in the image ...
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Post and steel rope framework for grape vine
I am planning to build a framework to support a grape vine above a patio. Ideally I would like to use steel rope to provide this framework, rather than a full timber frame.
Diagram attached.
There is ...
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Deflection of a log splitter beam
I'm designing a machine that can be simplified as a log splitter. It will have a long, central beam that will resist both the forces of a force pushing out and the moment that will be caused by the ...
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Finding the bending moment diagram for an indeterminate continuous beam
In a recent lecture, we had the following example of an indeterminate continuous beam where we must find the redundant support reaction at $A$:
This was found by removing the support at $A$, and then ...
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Stress and Displacement of Cantilever Plate with a Uniform Load
Does any one happen to know of any resources that describe the stress and displacement of a uniformly distributed load in the direction perpendicular to the length direction of a plate analytically? I ...
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Cantilever Beam Deflection under Plane strain
I have a university code that calculates the maximum deflection of cantilever beam of length, $L$ subjected to a point load, $P$ on its free end. The software assumes plane strain conditions. I ...
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How do I calculate kg/m for 5 boards sitting on 3 beams
I'm new to this, thank you for your patience,
I have some wooden boards that each weigh 5.5 kg with dimensions of 120 cm * 60 cm
I also have some wooden beams with dimensions of 3 meters length and 10 ...
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Is the maximum bending moment of a fixed end beam always at end?
Mathematically, we can see that with downward loads only (only upward loads at the ends), the maximum bending moment for a fixed end beam of span $L$ either occurs at $x=0$, $x=L$, or where the shear ...
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Bending analysis of beams with varying cross section
All problems I solved in MoM class regarding beam bending involved a beam with continuous cross section. But is the process the same for a beam with varying cross section? For 'same process' I mean ...
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Composite Beam Theory - Calculating torsion and beam deflection of a composite beam made up of a pipe inside a pipe
I am trying to calculate two things. First the beam deflection of my model after bending and second angle of twist after applying torque.
My model is composed of two tubes (cylindrical hollow beams). ...
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Compound angle for support tri-beam / double knee brace
I'm trying to determine the most structurally sound way to construct a support beam for a serious treehouse. There are four options I've mocked up below - the first two are individual knee brace ...
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Maximum Deflection for simply supported beam under arbitrary triangular loading
I am trying to get the:
maximum deflection
location of maximum deflection
deflection at any point
For a beam under an arbitrary triangular load (i.e. a, b, c, and w can vary). I tried to solve this ...
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How to convert multiple point loads to uniformly distributed load
So I am working on a project with variables on how many point loads may be applied over a single span.
Both ends are fixed, this is a constant.
For example, I may have a beam which is 6m in overall ...
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Timoshenko Fixed Fixed Total Beam Deflection
I am trying to solve a problem where there is a fixed-fixed (clamped-clamped) beam with a point load in the middle (at L/2). The L/H is less then the 10 required for normal beam bending analysis and ...
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How to find the location on the 2-support beam where the deflection will be biggest?
Consider the uniform indeterminate beam as shown above. This beam is to be subjected to a single, 80N point load (acting down ) somewhere along its length.
What is the procedure (i.e steps and logic) ...
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Does the inertia of a beam section include the material density?
Sorry but I'm a little rusty. When solving a beam of any type of section, must the density be included in the moment of inertia of the section?
For example, if I see Navier's formula, I would say ...
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Get Node Numbers to Variable
I am using Andys APDL.
I want to create Beam Element by entering Node numbers.
Nodes numbers selection is through option “by location“
Then I don’t know how use them in element creation command i.e. E,...
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deflection of mild steel hollow tube beam
I am trying to compute the deflection of a hollow tube of mild steel, and my computation seems to give radically different results than a couple of online calculators. Apparently one is in error.
The ...
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Horizontal "pinching" force of an arch with applied moment
I have some Shape Memory Alloy wire programmed to curl from a straight beam into a circle. The force this generates is approximated as a uniform distributed bending moment along the length of the wire....
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